Arrangement, Method and Sensor for Measuring an Absolute Angular Position Using a Multi-Pole Magnet

ABSTRACT

An arrangement for measuring an angular position of a rotor with respect to a stator, comprises a multi-pole magnet mounted on the rotor, and a sensor mounted on the stator and a plurality of sensor elements organized in two groups or four groups for measuring a magnetic field component. A method for calculating the angular position comprises making a sum of signals of the elements of each group, a ratio of the two sums, and an arctan function. Alternatively the method may comprise making a sum of signals, the difference of sums, a ratio of the differences, and an arctan function. An integrated sensor, and the use of such arrangement or sensor in an automotive environment.

FIELD OF THE INVENTION

The present invention relates to the field of position sensors using amagnetic field. More in particular, the present invention relates to acontactless arrangement and a method for precise determination of anangular position less than 360°, using a magnetic field.

BACKGROUND OF THE INVENTION

The measurement of rotation angle is required in various applications,such as manual electrical switches or position detection of a motor or avalve or the like. Depending on cost and accuracy constraints, this taskcan be accomplished by various methods, such as mechanical contacts,potentiometers, optical encoders, or magnetic encoders.

Modern integrated circuit technology offers the possibility to integratemagnetic sensors and their readout and angle calculation electronics ona single die. This allows providing detectors of mechanical rotationwhich consist of a permanent magnet attached to a rotor and amonolithically integrated sensor attached to a stator, at competitivecost and good performance. The absence of mechanical contact between therotor with the magnet and the stator with the sensor allows for hermeticencapsulation of the sensor. This permits wear-free angle measurementsunder harsh environmental conditions.

With the increase of compactness of electrical systems, particularly inautomobiles with the arrival of hybrid engine systems, such positionsensors are additionally exposed to external magnetic fields from nearbycurrent conductors carrying strong current (e.g. more than 100 A). Tomaintain high sensing accuracy under such conditions, the sensor can beshielded by a ferromagnetic shield, or it must be made intrinsicallyrobust towards such fields. This can be achieved by measuring a fieldgradient rather than an absolute field, since any external field isassumed constant in first approximation over the sensor as long as thesensor dimensions are small.

A sensor corresponding to this requirement is known from EP0916074B1. Itdescribes a method and arrangement for contactless angle measurementusing a magnetic field originating from a non rotation-symmetric magnet(in particular a two-pole magnet), whereby an axial field component (Bz)in parallel with the rotation axis is measured by sensor elements (socalled “Horizontal Hall elements”) at several separate spots inside aplane perpendicular to the rotation axis. Then the difference betweendiametrically opposed sensor element values is taken, such that anysignal from a constant external (disturbance) field is subtracted and itis not appearing anymore in the angle signal.

A disadvantage of the described method and arrangement is itsapplication for small angle measurement.

US20020021124 describes a position sensor using one or more so calledmagnetic field concentrators (abbreviated “IMC”) to bend magnetic fieldlines, in combination with either horizontal Hall elements located underthe IMC, or vertical Hall elements located tangentially to the edge ofthe IMC.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a sensor, and anarrangement and a method for measuring an absolute angular position of arotor with respect to a stator, that is substantially insensitive to anexternal magnetic field.

It is in particular an object of embodiments of the present invention toprovide such a sensor and arrangement and method for measuring anangular position smaller than 360° with an increased sensitivity.

This objective is accomplished by an arrangement, and method and sensoraccording to embodiments of the present invention.

In a first aspect, the present invention provides an arrangement formeasuring an angular position of a rotor with respect to a stator. Thearrangement comprises:

the rotor rotatable around a rotation axis;

the stator having a fixed position with respect to the rotation axis;

a magnetic source mounted on the rotor for creating a magnetic field,the magnetic source being a multi-pole magnet having at least fourmagnet poles and providing a periodically repetitive magnetic fieldpattern with respect to the rotation axis;

a sensor mounted on the stator and comprising a plurality of sensorelements for measuring at least one magnetic field component of themagnetic field and for providing a measurement signal indicative of theat least one magnetic field component, the sensor being locatedsubstantially centered around the rotation axis and being located in aplane substantially perpendicular to the rotation axis at a firstdistance from the magnetic source; the sensor elements being locatedsubstantially on a circle at a second distance from the rotation axis,and oriented for detecting the at least one magnetic field component;and

means for calculating the angular position of the rotor from theprovided sensor signals.

In a second aspect, the invention provides an arrangement for measuringan angular position of a rotor with respect to a stator. The arrangementcomprises the rotor rotatable around a rotation axis; the stator havinga fixed position with respect to the rotation axis; a magnetic sourcemounted on the rotor for creating a magnetic field, the magnetic sourcebeing a multi-pole magnet having a number of magnetic poles forgenerating a periodically repetitive magnetic field pattern with respectto the rotation axis, the number of magnetic poles being at least four;a sensor mounted on the stator and comprising a plurality of sensorelements for measuring at least one magnetic field component of themagnetic field and for providing a measurement signal indicative of theat least one magnetic field component, the sensor being locatedsubstantially centered around the rotation axis and being located in aplane substantially perpendicular to the rotation axis at a firstdistance from the magnetic source; the sensor elements being locatedsubstantially on a circle at a second distance from the rotation axis,and being oriented for detecting the at least one magnetic fieldcomponent; the plurality of sensor elements being partitioned in atleast a first group and a second group, the elements within each groupbeing located at equidistant angular positions on the circle, theangular distance between an element of the first group and an element ofthe second group being equal to 180° divided by the number of magneticpoles of the magnetic source; means for calculating the angular positionof the rotor from the provided signals, the means for calculating beingadapted for calculating a first sum or first average of the signalsprovided by the sensor elements of the first group, and for calculatinga second sum or second average of the signals provided by the sensorelements of the second group, and for determining the angular positionof the rotor based on one or more values selected from the groupconsisting of the first sum, the first average, the second sum and thesecond average.

It is an advantage of using a magnetic field for determining an angularposition that the sensor is contactless, thus there is no mechanicalcontact between a fixed and a movable part, thus no wear. Such sensorscan advantageously be used in harsh environments.

It is an advantage of using a single integrated sensor comprisingmultiple sensor elements, in that the risk of misalignment of individualsensor elements or several sensors is eliminated, and interconnectionsof those sensors can be omitted.

It is an advantage of such an arrangement that the first group ofelements is arranged for measuring a so called sine signal, while thesecond group of elements are arranged for measuring a cosine signal,together forming quadrature signals, from which the angular position canbe accurately determined.

It is an advantage of such an arrangement that it allows any of thetangential, radial or axial field components of the magnetic source tobe measured, instead of (only) axial field components.

It is an advantage of such an arrangement that it does not require theaddition of a ferromagnetic yoke to the stator, for shaping the magneticfield of the rotor, which would add component cost and labor.

It is an advantage of such an arrangement that the magnetic sourcecreates a magnetic field in close vicinity to the magnet and to therotation axis, where the magnetic field components at locations lying ona circle concentric with the rotation axis, and at a short distance fromthe magnet, has tangential and/or radial and/or axial field componentswhich vary in a substantially periodic, e.g. sine or cosine, manner withthe rotation angle, and in a substantially linear manner with distancefrom the rotation axis. Examples of such magnets are magnets having acylindrical shape with a square, circular or polygonal cross-section.

It is an advantage that the angular position provided by such anarrangement is or can be robust for (e.g. is substantially insensitiveto) position-offset errors. This offers the further advantage of nothaving to calibrate to compensate for position errors.

It is an advantage that the angular position provided by such anarrangement is or can be robust for (e.g. is substantially insensitiveto) a uniform external magnetic field.

The magnetic source may be a multi-pole disc with circular shape, squareshape or polygonal shape, e.g. hexagon. The multi-pole magnet may be,but does not need to be, provided with a central opening, for example acentral cylindrical opening (thus basically forming an annulus).

The number of sensor elements is at least equal to the number of polesof the magnetic source, but may also be twice that number, for improvedfunctionality.

In embodiments of the arrangement according to the present invention,the multi-pole magnet is a permanent magnet. The use of a permanentmagnet for generating a magnetic field has the advantage that no powerneeds to be applied for generating the magnetic field.

In embodiments of the arrangement according to the present invention,the multi-pole magnet has a central cylindrical opening.

In embodiments of the arrangement according to the present invention,the multi-pole magnet has at least six magnetic poles.

It is an advantage of such an arrangement that it offers a highersensitivity.

It is an advantage of an arrangement with a six-pole magnet, overmagnets with more poles, that the angular range is 0 to 120°. The moremagnet poles are available, the smaller the angular sensitivity rangebecomes.

In embodiments of the arrangement according to the present invention,the multi-pole magnet has a ring shape having an outer diameter and aninner diameter, and the circle in the sensor has a diameter of 1 to 30%of the outer diameter of the magnet.

It is an advantage of such arrangement that the diameter of the circlewhere the sensor elements are located, is substantially independent ofthe dimensions of the ring magnet. This allows the sensor and the magnetdimensions to be chosen substantially independent from each other. Thisalso allows further technology scaling of the sensor independent of themagnet.

In embodiments of the arrangement according to the present invention,the measured at least one magnetic field component comprises atangential field component of the magnetic field, oriented substantiallytangential to the circle.

It is an advantage that such a tangential field originating from amulti-pole ring magnet or disk shape magnet provides a substantiallysinusoidal signal in function of the angular distance between the statorand the rotor, and that the magnitude of the tangential field componentvaries in a substantially linear manner with distance from the rotationaxis, offering excellent position-offset correction, and allowingscaling of the technology.

In embodiments of the arrangement according to the present invention,the sensor elements comprise vertical Hall effect elements having aplate with a normal that is tangential to the circle.

It is an advantage that such Hall elements are ideally suited formeasuring (only) the tangential field component, while being insensitiveto the axial or radial field components.

It is an advantage of using vertical Hall effect elements, because theyare built in the depth direction of the semiconductor, e.g. silicon,substrate, and thus occupy less semiconductor area.

In embodiments of the arrangement according to the present invention,each sensing element comprises a pair of horizontal Hall effect elementslocated on the circle adjacent to each other, and having plates orientedsubstantially perpendicular to the rotation axis, and IMC segments forbending the local tangential magnetic field into a directionsubstantially perpendicular to the plates.

It is an advantage of such an arrangement that horizontal Hall elementscan be used, which provide higher sensitivity and feature a smalleroffset.

It is an advantage of using a horizontal Hall element in combinationwith IMC, in that the IMC provides for a signal amplification in apassive way.

In embodiments of the arrangement according to the present invention,the measured at least one magnetic field component comprises a radialfield component of the magnetic field, oriented substantially radiallyto the circle.

It is an advantage that such a radial field originating from amulti-pole ring magnet or disk shape magnet provides a substantiallysinusoidal signal in function of the angular distance between the statorand the rotor, and that the magnitude of the radial field componentvaries in a substantially linear manner with distance from the rotationaxis, offering excellent position-offset correction, and allowingscaling of the technology. The radial field and tangential field offerthe same advantages.

In such embodiments, the sensor elements may comprise vertical Halleffect elements having a plate with a normal that is perpendicular toand intersects with the rotation axis.

It is an advantage that such Hall elements are ideally suited formeasuring (only) the radial field component, while being insensitive tothe axial or tangential field components.

It is an advantage of using vertical Hall effect elements, because theyare built in the depth direction of the semiconductor, e.g. silicon,substrate, and thus occupy less semiconductor area.

It is a further advantage of using vertical Hall elements in that no IMCis required.

In embodiments of the arrangement according to the present invention,the means for calculating is adapted for calculating the ratio of thefirst sum and the second sum or the ratio of the first average and thesecond average, and for determining the angular position of the rotorbased on the arctangent or arccotangent of said ratio.

It is an advantage that the angular position can be calculated byrelatively simple arithmetic. The goniometric function may beimplemented by means of a look-up table, optionally with linearinterpolation. The table may be stored in non-volatile memory.

In embodiments of the arrangement according to the present invention,the number of sensor elements is twice the number of magnetic poles ofthe multi-pole magnet. The sensor further comprises a third group and afourth group of magnetic sensor elements located substantially on thecircle, the magnetic sensor elements of the third and fourth group beingoriented for detecting at least one magnetic field component. The sensorelements within each of the third and fourth group are located atequidistant angular positions on the circle, the angular distancebetween an element of the third group and an element of the first groupbeing equal to 2×180°=360° divided by the number of magnet poles of themagnetic source, and the angular distance between an element of thefourth group and an element of the first group being equal to3×180°=540° divided by the number of magnet poles of the magneticsource. The means for calculating is further adapted for calculating athird sum or third average of the signals provided by the elements ofthe third group, and for calculating a fourth sum or fourth average ofthe signals provided by the elements of the fourth group. The means forcalculating is further adapted for determining the angular position ofthe rotor based on one or more numbers selected from the groupconsisting of the first sum, the first average, the second sum, thesecond average, the third sum, the third average, the fourth sum and thefourth average.

It is an advantage of this embodiment that it may provide redundancy,which can be used to further increase the accuracy by averagingtolerances of the components, e.g. non-idealities the magnet field,misalignment of the integrated circuit, tolerances within the integratedcircuit, etc.

It is also an advantage of this embodiment that it can provide areliable measurement, or can indicate an error, e.g. when the twomeasured angles deviate more than a given threshold value, as the casemay be.

In embodiments of the arrangement according to the present invention,each sensor element comprises a horizontal Hall effect element, and thearrangement further comprises an integrated magnetic concentratorcomprising a central part located on top of the horizontal Hallelements, and a plurality of elongated parts located at a distance fromthe Hall elements and oriented in radial directions.

In embodiments of the arrangement according to the present invention,each sensor element comprises a horizontal Hall effect element, and thearrangement further comprises an integrated magnetic concentratorcomprising a central part, and a plurality of elongated parts eachlocated on top of one of the Hall elements and oriented in radialdirections.

In embodiments of the arrangement according to the present invention,the means for calculating is further adapted for calculating a firstdifference between the first sum and the third sum, and for calculatinga second difference between the second sum and the fourth sum. The meansfor calculating is further adapted for calculating the ratio of thefirst difference and the second difference, and for determining theangular position of the rotor based on the arctangent or arc cotangentof said ratio.

It is an advantage that by using this particular algorithm, that theangular position provided by such an arrangement is additionally robustfor (e.g. substantially insensitive to) a constant external fieldgradient, or in other words, insensitive to the zero and first orderterms of a non-uniform external magnetic field. In this way, themagnetic field caused by a current carrying conductor can beconsiderably reduced. This advantage cannot be underestimated,especially in an automotive environment, in particular under the hood.

In a third aspect of the present invention, a use is provided of such anarrangement for calculating an angular position in an automotiveenvironment.

It is particularly advantageous to use the proposed arrangement underthe hood, where substantially large currents flowing in conductors maycause large disturbance fields, since the arrangement is highlyinsensitive to both the zero order term as well as the first order termsthereof.

In a fourth aspect of the present invention, a method is provided fordetermining an angular position of a rotor with respect to a statorusing the arrangement as described above. The method comprises the stepsof: calculating a first sum or a first average of the signals providedby the first group of sensor elements; calculating a second sum orsecond average of the signals provided by the second group of elements;determining the angular position of the rotor based on one or morenumbers selected from the group consisting of the first sum, the firstaverage, the second sum and the second average.

In embodiments of the method according to the present invention, themethod further comprising the step of subtracting the signals of theelements of each pair so as to provide a combined signal for thecalculation of the first resp. second sum or first resp. second average.

Each pair of horizontal Hall elements in this configuration provide infact a single value.

In embodiments of the method according to the present invention, themethod further comprises: calculating the ratio of the first sum and thesecond sum or the ratio of the first average and the second average;determining the angular position of the rotor based on the arctangent orarc cotangent of said ratio.

In embodiments of the method according to the present invention, themethod further comprises: calculating a third sum or third average ofthe signals provided by the sensor elements of the third group, and forcalculating a fourth sum or fourth average of the signals provided bythe sensor elements of the fourth group; determining the angularposition of the rotor based on one or more numbers selected from thegroup consisting of the first sum, the first average, the second sum,the second average, the third sum, the third average, the fourth sum andthe fourth average.

In embodiments of the method according to the present invention, themethod further comprises a step of calculating a first differencebetween the first sum and the third sum, and a second difference betweenthe second sum and the fourth sum, and the ratio of the first differenceand the second difference; and determining the angular position of therotor based on the arctangent or arc cotangent of said ratio.

According to a fifth aspect, the present invention provides anintegrated sensor circuit for measuring an angular position of a rotorwith respect to a stator, the rotor being rotatable around a rotationaxis and comprising a magnetic source mounted on the rotor for creatinga magnetic field, the magnetic source being a multi-pole magnet having anumber of magnetic poles for generating a periodically repetitivemagnetic field pattern with respect to the rotation axis, the number ofmagnetic poles being at least four; the stator having a fixed positionwith respect to the rotation axis, the integrated sensor circuit beingmountable to the stator in the vicinity of the multi-pole magnet and inline with the rotation axis in a plane substantially perpendicular tothe rotation axis at a first distance from the magnetic source. Theintegrated sensor circuit comprises: a plurality of sensor elements,each sensor element being adapted for measuring at least one magneticfield component of the magnetic field and for providing a measurementsignal indicative of the strength of the at least one magnetic fieldcomponent at the location of the sensor element, the sensor elementsbeing located substantially on a circle at a distance from the rotationaxis, and being oriented for detecting the at least one magnetic fieldcomponent; the plurality of sensor elements being partitioned in a firstgroup and a second group, the elements within each group being locatedat equidistant angular positions on the circle, the angular distancebetween an element of the first group and an element of the second groupbeing equal to 180° divided by the number of magnet poles of themagnetic source; means for calculating the angular position of the rotorfrom the provided signals; and wherein the means for calculating isadapted for calculating a first sum or first average of the signalsprovided by the elements of the first group, and for calculating asecond sum or second average of the signals provided by the elements ofthe second group, and for determining the angular position of the rotorbased on one or more number selected from the group consisting of thefirst sum, first average, the second sum and the second average.

It is an advantage of such an integrated circuit that it provides anaccurate angular position, which is substantially insensitive or has areduced sensitivity to an external magnetic field, and which issubstantially insensitive or has a reduced sensitivity to positioningerrors of the integrated circuit with respect to the rotation axis,while providing an improved sensitivity. This integrated circuit isideally suited for measuring absolute angular positions in systems wherethe total angle is less than 360°, for example less than 180° in case a4-pole magnet is used, or less than 120° in case a 6-pole magnet isused, etc. This may provide a more accurate positioning e.g. inapplications like controlling a valve.

In embodiments of the integrated circuit according to the presentinvention, each sensor element comprises a vertical Hall effect elementhaving a plate with a normal that is tangential to the circle.

In embodiments of the integrated circuit according to the presentinvention, each sensing element comprise a pair of horizontal Halleffect elements located on the circle adjacent to each other, and havingplates oriented substantially perpendicular to the rotation axis, andIMC segments for bending the local tangential magnetic field into adirection substantially perpendicular to the plates.

In embodiments of the integrated circuit according to the presentinvention, each sensor element comprises a vertical Hall effect elementhaving a plate with a normal that is perpendicular to and intersectswith the rotation axis.

In embodiments of the integrated circuit according to the presentinvention, the means for calculating is further adapted for calculatingthe ratio of the first sum and the second sum or the ratio of the firstaverage and the second average and for determining the angular positionof the rotor based on the arctangent or arc cotangent of said ratio.

In embodiments of the integrated circuit according to the presentinvention, the number of sensor elements is twice the number of magneticpoles of the multi-pole magnet; and the integrated circuit furthercomprises a third group and a fourth group of magnetic sensor elementslocated substantially on the circle, the magnetic sensor elements of thethird and fourth group being oriented for detecting at least onemagnetic field component, the sensor elements within each of the thirdand fourth group being located at equidistant angular positions on thecircle, the angular distance between an element of the third group andan element of the first group being equal to 2×180°=360° divided by thenumber of magnet poles of the magnetic source, and the angular distancebetween an element of the fourth group and an element of the first groupbeing equal to 3×180°=540° divided by the number of magnet poles of themagnetic source; and the means for calculating is further adapted forcalculating a third sum or third average of the signals provided by theelements of the third group, and for calculating a fourth sum or fourthaverage of the signals provided by the elements of the fourth group; andthe means for calculating is further adapted for determining the angularposition based on one or more numbers selected from the group consistingof the first sum, the first average, the second sum, the second average,the third sum, the third average, the fourth sum and the fourth average.

In embodiments of the integrated circuit according to the presentinvention, each sensor element comprises a horizontal Hall effectelement, and the integrated circuit further comprises an integratedmagnetic concentrator comprising a central part located on top of thehorizontal Hall elements, and a plurality of elongated parts located ata distance from the Hall elements and oriented in radial directions.

In embodiments of the integrated circuit according to the presentinvention, each sensor element comprises a horizontal Hall effectelement, and the integrated circuit further comprises an integratedmagnetic concentrator comprising a central part and a plurality ofelongated parts each located on top of one of the Hall elements andoriented in radial directions.

In embodiments of the integrated circuit according to the presentinvention, the means for calculating is further adapted for calculatinga first difference between the first sum and the third sum, and forcalculating a second difference between the second sum and the fourthsum; and the means for calculating is further adapted for calculatingthe ratio of the first difference and the second difference, and fordetermining the angular position of the rotor based on the arctangent orarc cotangent of said ratio.

In a sixth aspect of the present invention, a use is provided of such anintegrated circuit for calculating an angular position in an automotiveenvironment.

Particular and preferred aspects of the invention are set out in theaccompanying independent and dependent claims. Features from thedependent claims may be combined with features of the independent claimsand with features of other dependent claims as appropriate and notmerely as explicitly set out in the claims.

These and other aspects of the invention will be apparent from andelucidated with reference to the embodiment(s) described hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a prior art arrangement for absolute angular positionmeasurement using a two-pole bar magnet.

FIG. 2 shows an arrangement for absolute angular position measurementaccording to embodiments of the present invention, using a four-polemagnet. A constant external field is also shown.

FIG. 3 shows an axially magnetized ring-magnet with twelve poles andwith a central cylindrical opening, as can be used in embodiments of thepresent invention.

FIG. 4 shows an axially magnetized ring-magnet with four poles, and witha central cylindrical opening, as can be used in embodiments of thepresent invention.

FIG. 5 shows a disk magnet without a central opening, having a surfacemagnetization forming four pole pairs (eight poles), as can be used inembodiments of the present invention.

FIG. 6 shows an example of a multi-pole ring-magnet with a centralopening, and having two pole-pairs, shown in top-view (bottom of FIG. 6)and shown in side-view (top of FIG. 6). FIG. 6 also shows the positionof sensor elements in a plane located at a distance from the magnet, andoriented perpendicular to the rotation axis.

FIG. 7 shows a simulation of the tangential field component of thefour-pole ring magnet of FIG. 6 at a distance of 3 mm below the magnetsurface. The outer and middle circles correspond to the outer resp.inner diameter of the ring magnet. The inner circle corresponds to animaginary circle where the sensor elements could be placed.

FIG. 8 shows an example of the position and orientation of four verticalHall sensor elements, lying on the imaginary circle, and oriented formeasuring the tangential magnetic field component of FIG. 7.

FIG. 9 shows a simulation of the radial field component of the four-polering magnet of FIG. 6 at a distance of 3 mm below the magnet surface.The same rings as in FIG. 7 are shown.

FIG. 10 shows an example of the position and orientation of fourvertical Hall sensor elements of a sensor according to embodiments ofthe present invention, the elements lying on an imaginary circle, andoriented for measuring the radial magnetic field component of FIG. 9.

FIG. 11 shows a simulation of the axial field component of the four-polering magnet of FIG. 6 at a distance of 3 mm below the magnet surface.The same rings as in FIG. 7 are shown.

FIG. 12 shows an example of the position and orientation of fourhorizontal Hall sensor elements of a sensor according to embodiments ofthe present invention, the elements lying on an imaginary circle, andoriented for measuring the axial magnetic field component of FIG. 11.

FIG. 13 shows the strength of the axial magnetic field component of FIG.11 in function of radius.

FIG. 14 shows the strength of the radial magnetic field component ofFIG. 9 in function of radius.

FIG. 15 shows the strength of the tangential magnetic field component ofFIG. 7 in function of radius.

FIG. 16 shows a six-pole ring magnet with a central cylindrical opening.Some field lines are shown on the outside of the ring-magnet, althoughthe magnetic field is not measured there, but rather below the magnet.Three bold black arrows indicate the orientation of a first group ofthree sensor elements (not shown), three bold white arrows indicate theorientation of a second group of three sensor elements (not shown), allsensor elements being adapted for measuring the tangential fieldcomponent of the magnetic field.

FIG. 17 shows an example of the position and orientation of six verticalHall sensor elements of a sensor according to embodiments of the presentinvention, the elements lying on an imaginary circle, and adapted formeasuring the tangential magnetic field component of the magnet of FIG.16 in an arrangement as shown in FIG. 2.

FIG. 18 shows an example of sine and cosine signals which can beobtained from the sensor elements of FIG. 17 when used in combinationwith the six-pole magnet of FIG. 16.

FIG. 19 shows an embodiment of a sensor having pairs of horizontal Hallplate elements and Integrated Magnetic Concentrators (IMC) as can beused in conjunction with the six-pole ring magnet of FIG. 16.

FIG. 20 shows the same six-pole ring magnet with a central cylindricalopening as shown in FIG. 16. Three bold black arrows indicate theorientation of a first group of three sensor elements (not shown), threebold white arrows indicate the orientation of a second group of threesensor elements (not shown), all sensors being adapted for measuring theradial field component.

FIG. 21 shows an example of the position and orientation of six verticalHall sensor elements of a sensor according to embodiments of the presentinvention, the elements lying on an imaginary circle, and adapted formeasuring the radial magnetic field component of the magnet of FIG. 20in an arrangement as shown in FIG. 2.

FIG. 22 shows an example of sine and cosine signals which can beobtained from the sensor elements of FIG. 21.

FIG. 23 shows an example of a sensor having twelve vertical Hall sensorelements, oriented for measuring the radial magnetic field component ofa six-pole magnet. It has twice the number of sensor elements of thesensor of FIG. 21, which can be used for increased accuracy orreliability check. In another embodiment, this same arrangement but withother arithmetic, can also be used for measuring the angular position ina way which is substantially insensitive to an external constant field,and to an external constant field gradient.

FIG. 24 shows the arrangement of FIG. 2, but instead of the constantexternal field, an external field caused by a current conducting wire,is shown.

FIG. 25 is a variant of the sensor of FIG. 23, having twelve verticalHall sensor elements, oriented for measuring the tangential magneticfield component of the six-pole magnet of FIG. 16, which issubstantially robust against a constant external field and/or anexternal field with a constant gradient in any direction.

FIG. 26 shows an embodiment of a sensor with twelve horizontal Hallelements and Integrated Magnetic Concentrators comprising a central diskand a plurality of elongated strips, according to the present invention,the Hall elements being arranged under the central disk.

FIG. 27 shows a variant of the embodiment of the sensor shown in FIG.26, the Hall elements being arranged under the elongated strips.

FIG. 28 shows an arrangement of eight sensor elements according toaspects of the present invention, for use in conjunction with afour-pole ring magnet shown in FIG. 4.

The drawings are only schematic and are non-limiting. In the drawings,the size of some of the elements may be exaggerated and not drawn onscale for illustrative purposes.

Any reference signs in the claims shall not be construed as limiting thescope.

In the different drawings, the same reference signs refer to the same oranalogous elements.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The present invention will be described with respect to particularembodiments and with reference to certain drawings but the invention isnot limited thereto but only by the claims. The drawings described areonly schematic and are non-limiting. In the drawings, the size of someof the elements may be exaggerated and not drawn on scale forillustrative purposes. The dimensions and the relative dimensions do notcorrespond to actual reductions to practice of the invention.

The terms first, second and the like in the description and in theclaims, are used for distinguishing between similar elements and notnecessarily for describing a sequence, either temporally, spatially, inranking or in any other manner. It is to be understood that the terms soused are interchangeable under appropriate circumstances and that theembodiments of the invention described herein are capable of operationin other sequences than described or illustrated herein.

Moreover, the terms top, under and the like in the description and theclaims are used for descriptive purposes and not necessarily fordescribing relative positions. It is to be understood that the terms soused are interchangeable under appropriate circumstances and that theembodiments of the invention described herein are capable of operationin other orientations than described or illustrated herein.

It is to be noticed that the term “comprising”, used in the claims,should not be interpreted as being restricted to the means listedthereafter; it does not exclude other elements or steps. It is thus tobe interpreted as specifying the presence of the stated features,integers, steps or components as referred to, but does not preclude thepresence or addition of one or more other features, integers, steps orcomponents, or groups thereof. Thus, the scope of the expression “adevice comprising means A and B” should not be limited to devicesconsisting only of components A and B. It means that with respect to thepresent invention, the only relevant components of the device are A andB.

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure or characteristicdescribed in connection with the embodiment is included in at least oneembodiment of the present invention. Thus, appearances of the phrases“in one embodiment” or “in an embodiment” in various places throughoutthis specification are not necessarily all referring to the sameembodiment, but may. Furthermore, the particular features, structures orcharacteristics may be combined in any suitable manner, as would beapparent to one of ordinary skill in the art from this disclosure, inone or more embodiments.

Similarly it should be appreciated that in the description of exemplaryembodiments of the invention, various features of the invention aresometimes grouped together in a single embodiment, figure, ordescription thereof for the purpose of streamlining the disclosure andaiding in the understanding of one or more of the various inventiveaspects. This method of disclosure, however, is not to be interpreted asreflecting an intention that the claimed invention requires morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive aspects lie in less than allfeatures of a single foregoing disclosed embodiment. Thus, the claimsfollowing the detailed description are hereby expressly incorporatedinto this detailed description, with each claim standing on its own as aseparate embodiment of this invention.

Furthermore, while some embodiments described herein include some butnot other features included in other embodiments, combinations offeatures of different embodiments are meant to be within the scope ofthe invention, and form different embodiments, as would be understood bythose in the art. For example, in the following claims, any of theclaimed embodiments can be used in any combination.

In the description provided herein, numerous specific details are setforth. However, it is understood that embodiments of the invention maybe practiced without these specific details. In other instances,well-known methods, structures and techniques have not been shown indetail in order not to obscure an understanding of this description.

When reference is made to “external (unwanted) magnetic field”, themagnetic field other than that caused by the “magnetic source” mountedto the rotor, e.g. a permanent magnet, is meant.

With a magnetic source having a “rotation symmetrical” field is meantthat the magnetic field looks the same after the magnetic source isrotated around its axis with a angle smaller than 360°, e.g. 180° for afour-pole ring magnet or disk magnet, or 120° for a six-pole ring magnetor disk magnet, etc.

With a uniform external field is meant a field with a constant amplitudeand a constant direction. Such a field can be described as a constantvector (Bxo, Byo, Bzo).

FIG. 1 shows a prior art arrangement for absolute angular positionmeasurement using a two-pole bar magnet, as described in EP0916074B1.The arrangement has a rotor 22 rotating around a rotation axis 21 withrespect to a stator 27. A bar magnet 23 is mounted to the rotor 22 forcreating a magnetic field, some flux-lines of which are shown. At adistance “below” the magnet (z-direction), a sensor is located, thesensor having four sensor elements 24, 25, 26, three of which are shown.The sensor elements are Hall elements for sensing an axial fieldcomponent B_(⊥) of the magnetic field, e.g. field lines oriented in thevertical Z direction, in parallel to the rotation axis. It is explicitlymentioned in the description and the claims of EP0916074B1, that thesensor elements are to be organized in at least two sensor pairs, or toincrease accuracy in multiple pairs, and that the magnetic field has norotational symmetry relative to the rotation axis.

FIG. 2 shows an arrangement 1 comprising a sensor 6, in this case anintegrated circuit, for absolute angular position measurement of therotor 2 with respect to a stator (not shown), whereto the sensor 6 isfixedly mounted. The rotor 2 is rotatable around a rotation axis 4, andcomprises a multi-pole magnet 5 having at least four magnetic poles,Np=4, in this case a permanent disk-magnet having four poles (indicatedin light grey and dark grey). This magnet 5 creates, at a predetermineddistance, or in a predetermined distance range, a periodicallyrepetitive flux density pattern, e.g. a sinusoidal flux density pattern,of at least one of the three cylindrical components (radial, tangential,axial) of the magnetic field. The magnetic field is rotation symmetricwith respect to the rotation axis 4, and repeats itself with a period of180°, in this example. This implies that the angle sensor can onlymeasure mechanical angles in the range of 0° to 180°. For a six-polemagnet, the measurable range is 0° to 120°, etc.

The sensor 6 is arranged at a distance d1 “below” the magnet 5, and islocated substantially in line with the rotation axis 4, and is locatedin a plane β substantially perpendicular to the rotation axis 4. Thesensor 6 comprises at least four sensor elements located in a plane βsubstantially perpendicular to the rotation axis 4, for measuring one ormore magnetic field components Br, Bt, Bz, and means for calculating theangular position α of the rotor 2 from the signals provided by thosesensor elements, as will be described further. In embodiments of thepresent invention, the distance d1 is between zero and the outerdiameter of the magnet 5. In particular embodiments, the distance d1 maybe selected to be between 10 and 30% of the outer magnet diameter. Ifthe magnet is not circular shaped, the diameter may be the diameter of acircumscribing circle. Alternatively, for non-circular shaper magnets,the distance d1 may be between zero and the side length of the magnet,the side length being the length of the largest side of the magnet.

FIG. 3 to FIG. 5 show just a few examples of types of multi-pole magnets5 that can be used with the sensor 6 of FIG. 2, but many more types maybe used, as long as the magnet 5 is a multi-pole magnet having at leastfour poles (North and South poles), for creating a rotation-symmetricalmagnetic field B around the rotation axis 4, the field having tangentialand/or radial and/or axial field components Bt, Br, Bz respectively,which, when measured on an imaginary circle having a center at therotation axis 4, and located at a distance d1 from the magnet, varies ina substantially sinusoidal or cosinusoidal way with the angle α, andwhich preferably also varies in a substantially linear, e.g. in a linearway from the centre of the imaginary circle, to a certain radius value.The latter will be illustrated further in FIGS. 13 to 15.

FIG. 3 shows an axially magnetized ring-magnet with twelve poles (sixpole pairs) and with a central cylindrical opening, as can be used inembodiments of the present invention. It is to be noted that the numberof poles, twelve in the embodiment illustrated, is just an example, andring magnets having four poles (see FIG. 4), six poles (see FIG. 16 andFIG. 20), eight pole (see FIG. 5), ten poles, or even more, in general 2k poles, k being an integer larger than 1, may also be used inaccordance with embodiments of the present invention. However, themaximum angle α that can be measured decreases as the number of polesincreases, according to the formula: 720°/Np, whereby Np is the numberof poles.

FIG. 5 shows a disk magnet 5 without a central opening, and having asurface magnetization (in the example shown, the top surface). However,as can be appreciated when drawing field lines (not shown) from eachN-pole to the neighboring S-pole, this magnet indeed creates such amagnetic field with a tangential field component satisfying the abovecharacteristics. As can be appreciated from comparing FIG. 3, FIG. 4 andFIG. 5, a central opening in the magnet is not required; the magnet canalso be a disk magnet. In yet alternative embodiments, the magnet doesnot need to have a circular shape: it can have a square shape or apolygon shape. The magnet may even have slots. An important feature ofthe magnet is the repetitive flux field, e.g. sinusoidal with a periodof 720°/Np, Np being the number of poles of the magnet, of the radial Brand/or tangential Bt and/or axial Bz field component under rotation.

In what follows, it will be assumed that the magnet 5 is a multi-polering magnet, but as already explained, the invention is not limited toring magnets.

FIG. 6 shows an embodiment of a four-pole ring-magnet with a centralopening, and having four poles (two North poles, and two South poles),shown in top-view (lower part of FIG. 6) and shown in side-view (upperpart of FIG. 6). In a specific example, the ring magnet 5 may have anouter diameter OD of about 12 mm, an inner diameter ID of about 8 mm,and a height h of about 4 mm, but the invention is not limited thereto.The position of the sensor elements relative to the magnet is alsoshown, albeit not on scale, for illustrative purposes. The sensorelements E are located substantially at a distance d1 from the flatbottom surface of the magnet 5, and are located substantially on animaginary circle (not shown) located in a plane β perpendicular to therotation axis 4, having a center point on the rotation axis 4 and havinga diameter d2. This example will be described in detail. The skilledperson can then perform the same tests, simulations or measurements forother magnet types, or dimensions.

First Algorithm

FIG. 7 shows simulation results of the tangential magnetic fieldcomponent Bt of the magnetic field created by the four pole ring magnetof FIG. 6, measured at a distance d1 of 3 mm below the magnet surface.The simulation results are obtained by a 3D magnetic simulation with afinite element simulation tool. On top of the simulation result, threecircles are drawn, the outer circle and middle circles correspond to theouter resp. inner diameter of the ring magnet 5 (in the example having adiameter of 12 and 8 mm respectively). The inner circle 8 represents anexample of an imaginary circle 8 where the sensor elements could beplaced. It is to be noted that in the prior art, ring magnets are usedfor pulse encoding (e.g. counting the integer number of poleoccurrences, not fractions thereof), but as far as known to theinventor, the sensor is then always located under or outside of the ringmagnet, never “on the inside” of the ring (i.e. at a radial distancesmaller than the inner diameter of the magnet), despite the fact thatthe magnetic field component is the largest between the middle and outercircle (in the example the circles having a diameter of 8 and 12 mmrespectively). In addition, it is counter-intuitive to believe that thefield lines behave in a linear way near the centre of the ring, letalone at an axial distance d1 therefrom. It is to be noted that thismagnetic field can be generated by a single magnet 5, and that noferromagnetic yokes or the like are required (see also FIG. 6). Thisdecreases component cost and manufacturing cost, and decreases the riskfor misalignments.

FIG. 8 shows a first embodiment of a sensor having four sensor elementsVH1-VH4, in this case vertical Hall sensor elements, oriented formeasuring a tangential field Bt to the imaginary circle 8. In thisexample, the sensor elements are arranged in two groups: a first group Sconsisting of the sensor elements VH2 and VH4, and a second group Tconsisting of the sensor elements VH1 and VH3. The sensor elements VH2,VH4 of the first group S provide the signals S1, S2 respectively. Thesensor elements VH1, VH3 of the second group T provide the signals T1,T2 respectively. The signals S1 and S2 of the first group are added (notsubtracted as in EP0916074B1) to form a first sum sum1, the signals T1and T2 of the second group are added to form a second sum sum2:

sum1=S1+S2;  (1)

sum2=T1+T2;  (2)

The sensor elements within each group S, T are located equidistantly,e.g. at an angular distance of 720°/Np=e.g. 180° apart for a four-polemagnet, e.g. VH1 and VH3 are located 180° apart, as well as VH2 and VH4.

The angular distance between an element VH2 of the first group S and anelement VH1 of the second group T is equal to 180° divided by the numberNp of magnetic poles of the magnetic source 5, e.g. the angular distancebetween VH2 and VH1 is 180°/4=45°.

By positioning the sensor elements VH1 and VH3 at 180° apart, and thesensor elements VH2 and VH4 180° apart (in general 720°/Np, where Np isthe number of poles, in the example Np=4), and a sensor element VH2 ofthe first group S at an angular distance of 180°/Np=45° with respect toan element VH1 of the second group T, the value of sum1 varies like asine function of the number of pole pares multiplied by the positionangle of the rotor 2, e.g. twice the position angle of the rotor 2, i.e.2α in case of four poles as in the example illustrated, or 3α in case ofa six-pole magnet, and the value of sum2 varies as a cosine function ofthe number of pole pares multiplied by the position angle of the rotor2, e.g. 2α in case of a four-pole magnet, or 3α in case of a six-polemagnet, apart from a predefined offset, which can be determined duringmanufacturing, or can be measured during calibration, and is not takeninto account further. One can then calculate a ratio R as (for theexample illustrated):

R=sum1/sum2=tan(2α)  (3)

and the angle α can then be calculated as:

α=(arctan R)/2.  (4a)

Alternatively, the angle α may also be calculated as:

α=(arccotan(sum2/sum1))/2  (4b)

or by using equivalent formulas.

It is to be noted that instead of calculating the sum of the values ofeach group S, T, one could also calculate the average value of eachgroup, and calculate the ratio of the first average avg1 and the secondaverage avg2, etc, which would yield the same result for the angularposition α, since the average is sum divided by 2, and thus the ratio Rwould remain unchanged.

The configuration of FIG. 8 is substantially insensitive (or at leasthas a reduced sensitivity) to position-offset errors of the sensor 6with respect to the axis of rotation 4, because the signals T1 and T2generated by VH1 and VH3 (at least partially) compensate each other: ifone signal is larger due to radial position offset, the other issmaller, preferably by the same amount. The same applies for the signalsS1 and S2 provided by the sensors VH2 and VH4. For offset along the axisof rotation 4, hence in the z-direction, both sums (S1+S2) and (T1+T2)will be increasing or decreasing by the same factor, so that the ratiobetween them which is used for the angle calculation is not affected.

The configuration of FIG. 8 is also insensitive to a uniform externalmagnetic field Bext (see FIG. 2), because the values measured by thesensors in each group, cancel each other when being added, since thesensor elements VH1 and VH3 on the one hand, and VH2 and VH4 on theother hand, are oriented in opposite directions. Due to the fact that aratio R is taken of the sum or average of the field components, theabsolute value of the magnetic field components is irrelevant, onlytheir relative values matter. This means that the method is highlyrobust against ageing, tolerances on magnets, and temperature. Since fora four-pole magnet, the sine and cosine functions vary with 2α insteadof α, α being the mechanical angle over which the rotor is rotatedw.r.t. the stator, the sensor 6 with the four-pole magnet has a highersensitivity than the sensor of the prior art, despite the fact that ithas the same number of sensor elements. On the other hand, the angularposition range which can be measured by the sensor is 180°. The sensingelements VHi, i=1 to 4 of FIG. 8 are considered to be located in asingle plane β (see FIG. 2), even though the “Hall plates” of the sensorelements VHi would actually be built in the depth direction of thesubstrate. However, as the centers of the Hall plates are located on theimaginary circle 8, and as the relative dimensions of the Hall platesare much smaller (e.g. a factor 10 or more) than the diameter of theimaginary circle 8, the sensor elements can be considered as beinglocated in the plane β, without taking the “height” as measured in theaxial direction Z into account.

FIG. 9 shows simulation results (using the same tool and parameters asfor FIG. 7) of the radial magnetic field component Br of the magneticfield B created by the four-pole ring magnet of FIG. 6, measured at adistance d1 of about 3 mm below the magnet surface. On top of thesimulation result, the same three circles are drawn as shown in FIG. 7.It is to be noted that this magnetic field is generated by a singlemagnet 5, and that no ferromagnetic yokes or the like are required (seealso FIG. 6). This decreases component cost and manufacturing cost, anddecreases the risk for misalignments.

FIG. 10 shows a second embodiment of a sensor having four sensorelements VHi, i=1 to 4, in this case vertical Hall sensor elements,oriented for measuring a radial field on the imaginary circle 8. Thesensor elements are again arranged in two groups: a first group Sconsisting of the sensor elements VH2 and VH4, and a second group Tconsisting of the sensor elements VH1 and VH3. The sensor elements VH2,VH4 of the first group S provide the signals S1, S2 respectively. Thesensor elements VH1, VH3 of the second group T provide the signals T1,T2 respectively. The signals S1 and S2 of the first group are added (notsubtracted as in EP0916074B1) to form a first sum sum1, the signals T1and T2 of the second group are added to form a second sum sum2.

sum1=S1+S2;  (5)

sum2=T1+T2;  (6)

By positioning the sensor elements VH1 and VH3 at 180° apart, and thesensor elements VH2 and VH4 180° apart (in general 720°/Np, where Np isthe number of poles, in the example Np=4), and a sensor element VH2 ofthe first group S at an angular distance of 180°/Np=45° with respect toan element VH1 of the second group T, the value of sum1 varies, in the4-pole embodiment illustrated, like a sine function of twice theposition angle of the rotor 2, i.e. 2α, and the value of sum2 varies asa cosine function of 2α, apart from a predefined offset.

One can then calculate a ratio R as:

R=sum1/sum2=tan(2α)  (7)

and the angle α can then be calculated as:

α=(arctan R)/2  (8)

As mentioned above, the angle α may also be calculated using thearccotan function.

It is to be noted that instead of calculating the sum of the values of agroup, one could also calculate the average value of each group S, T,calculate the ratio R of the averages, etc, which would yield the sameresult for the angular position α, since the average is sum divided by2, and thus the ratio R would remain unchanged.

The configuration of FIG. 10 is substantially insensitive toposition-offset errors of the sensor 6 w.r.t. the magnet 5, because thesignals S1, S2 generated by VH2 and VH4 compensate each other when beingadded: if one signal is larger due to radial position offset, the otheris smaller, preferably by the same amount. The same applies for VH1 andVH3. The configuration of FIG. 10 is also insensitive to a uniform (e.g.constant) external magnetic field Bext, because the values measured bythe sensors in each group cancel each other (since the sensor elementsare oriented in opposite directions). Due to the fact that a ratio istaken of the sum or average of the field components, the absolute valueof the magnetic field components is irrelevant, only their relativevalues. This means that the method is highly robust against ageing,tolerances on magnets, and temperature.

FIG. 11 shows simulation results of the axial field component Bz of themagnet of FIG. 6 at a distance of 3 mm below the magnet surface. Thesame rings as in FIG. 7 are shown. At first sight the field looks muchlike the tangential field shown in FIG. 7 or the radial field shown inFIG. 9, but there is a slight disadvantage, which will be described inrelation to FIG. 12.

FIG. 12 shows a third embodiment of a sensor having four sensor elementsHH1 to HH4, in this case horizontal Hall sensor elements, oriented formeasuring an axial field on the imaginary circle 8. The sensor elementsare again arranged in two groups: a first group S consisting of thesensor elements HH1 and HH3, and a second group T consisting of thesensor elements HH2 and HH4. It is to be noted that all sensor elementsof a same group S or T which are in this embodiment located 720°/4=180°apart, e.g. the elements HH1 and HH3 of the first group S or HH2 andHH4, are oriented such that that generate a value with the same sign forthe same field direction (e.g. positive for field into the plane). Thegroups S, T are independent from one another, so both groups can havethe same orientation or can have a different orientation.

The sensor elements HH1, HH3 of the first group S provide the signalsS1, S2 respectively. The sensor elements HH2, HH4 of the second group Tprovide the signals T1, T2 respectively. The signals S1 and S2 of thefirst group are added (not subtracted as in EP0916074B1) to form a firstsum1, the signals T1 and T2 of the second group are added to form asecond sum2.

sum1=S1+S2;  (9)

sum2=T1+T2;  (10)

By positioning the sensor elements HH1 and HH3 at equidistant angularpositions, e.g. 180° apart, and the sensor elements HH2 and HH4 180°apart (in general 720°/Np, where Np is the number of poles, in theexample Np=4), and a sensor element HH1 of the first group S at anangular distance of 180°/Np=45° with respect to an element HH2 of thesecond group T, the value of sum1 varies like a sine function of twicethe position angle of the rotor 2, i.e. 2α, and the value of sum2 variesas a cosine function of 2α, apart from a predefined offset.

One can then calculate a ratio R as:

R=sum1/sum2=tan(2α)  (11)

and the angle α can then be calculated as:

α=(arctan R)/2  (12)

As mentioned above, the angle α may also be calculated using thearccotan function.

It is to be noted that instead of calculating the sum of the values of agroup, one could also calculate the average value of each group, and theratio of the averages, etc, which would yield a similar result. Theconfiguration of FIG. 12 is somewhat sensitive to position-offset errorsof the sensor 6 w.r.t. the magnet 5, as will be explained in relation toFIG. 13. Due to the fact that a ratio is taken of the sum or average ofthe field components, the absolute value of the magnetic fieldcomponents is irrelevant, only their relative values count. This meansthat the method is highly robust against ageing, tolerances on magnets,and temperature. A drawback of this embodiment, however, is that theconfiguration of FIG. 12 is very sensitive to a uniform (e.g. constant)external magnetic field Bext, because the values measured by the sensorsin each group do not cancel each other out (since the sensor elementsare oriented in the same direction). However, since there are onlyhorizontal Hall elements used, they are only sensitive to on external Bzfield, not to Bx, By.

By means of FIG. 7 to FIG. 12 it is explained that an arrangementcomprising a four-pole ring magnet and four sensor-elements, arranged onan imaginary circle, and oriented for measuring one field component Br,Bt, Bz, whereby the sensor elements are partitioned in two groups S, T,whereby the elements of each group S, T are oriented in oppositedirections (in case of Br and Bt) or in the same direction (in case ofBt), and whereby the elements in each group are located at equidistantpositions, and the positions of the groups are 45° apart, can be used todetermine the angular position of the sensor with respect to the magnet,by calculating the arctangent or arccotangent of the ratio R of the sum,or average of the signals of the elements of each group.

The position error sensitivity of these sensors, in particular theradial position sensitivity, will be described next, in relation to FIG.13 to FIG. 15.

FIG. 13 shows the strength of the axial magnetic field component Bz ofFIG. 11, measured on the line A-A, in function of the radius r. Thevertical axis shows the magnetic flux density (in T). As shown, thefield behaves in a very non-linear way near the centre, and behaves in alinear manner in a region from about 2.0 to about 4.0 mm from thecentre, where the field strength ranges from about 15 to 40 mT. In orderto place the sensor elements HH1 to HH4 of FIG. 12 such that they arehighly insensitive to position-offset, the sensor elements would have tobe located in these linear regions, e.g. the imaginary circle would needto have a diameter of about 4 to 8 mm. However, this limits thedown-scaling of sensor-technology (e.g. CMOS-technology), and prohibitsthat the sensor dimensions can be chosen independently from themagnet-dimensions, due to the relation between the magnet dimensions,and the position of the linear regions. Despite of not being perfect inrelation to position-offset-error, the sensor of FIG. 12, even if thediameter of the imaginary circle would be chosen in the “non-linear”region (e.g. less than 4 mm in the embodiment illustrated), would stillbe able to measure the angular position, in the absence of an externalmagnetic field, e.g. when being shielded. Furthermore, it is mentionedthat the function Bz(r) is “nearly” linear at a distance of about 1 mmto about 2 mm from the center, which deviation may well be acceptable inmost applications. And even within the range of 0 mm to 1 mm, the slopeof the curve is negative on the left of the center, and positive on theright, thus there is always at least a partial compensation againstoffset error.

FIG. 14 shows a similar drawing for the strength of the radial magneticfield component Br of FIG. 9 in function of radius, measured on the lineA-A. It is to be noted that a smaller portion is drawn (from −3 to +3mm). As can be seen, the field strength Br(r) is highly linear near thecenter, the linear range extends from about −1.5 to about +1.5 mm, andthe field strength Br ranges from 0 mT to about 17 mT. When the sensorelements are located in the area indicated by the grey rectangle, sensorelements of each group will compensate or cancel position offset. Sincethis rectangle includes the center, the distance d2 between the sensorelements can be made as small as desired, thus the die size of anintegrated circuit has no impact on the position error (also known as“off-axis error”), and can be chosen independently from the magnetdimensions. Suitable diameters d2 for the imaginary circle 8 of a sensorfor measuring this field component Br would be any diameter between 0.0(not included, but the diameter can go down to a few microns) and 3.0mm, in practice from 0.1 to 3.0 mm, e.g. about 0.5 mm, about 1.0 mm,about 1.5 mm, about 2.0 mm, or about 2.5 mm, or any values in between.The smaller the distance between two opposite sensor elements, thesmaller the signal. So the optimum would be as large as possible withinthe linear range for a typical semiconductor, e.g. silicon, die between1 and 10 mm². Practically the ring diameter is then between 1 and 3 mm.However, if a diameter d2 of 1.0 mm is chosen, the maximum positionoffset which can be compensated is 0.5 mm, half the diameter.

FIG. 15 shows a similar drawing for the strength Bt(r) of the tangentialmagnetic field component Bt of FIG. 7 in function of radius, measured onthe line A-A. It is to be noted that a portion is drawn from −4 to +4mm. As can be seen, the field strength is highly linear near the center,the linear range extends from about −2.5 to about +2.5 mm, and the fieldstrength Bt ranges from 0 mT to about 27 mT. When the sensor elementsare located in the area indicated by the rectangle, sensor elements ofeach group will compensate or cancel position offset. Since thisrectangle includes the center, the distance d2 between the sensorelements can be made as small as desired, thus the die size of anintegrated circuit has no impact on the position error (also known as“off-axis error”), and can be chosen independently from the magnetdimensions. Suitable diameters d2 for the imaginary circle 8 of a sensorfor measuring this field component Bt would be any diameter between 0.0and 5.0 mm, in practice from 0.1 to 5.0 mm, e.g. about 0.5 mm, about 1.0mm, about 1.5 mm, about 2.0 mm, about 2.5 mm, about 3.0 mm, about 3.5mm, about 4.0 mm, about 4.5 mm, or any values in between. However, if adiameter d2 of 1.0 mm is chosen, the maximum position offset which canbe compensated is 0.5 mm, half the diameter.

When comparing FIG. 14 and FIG. 15, it is to be noted that the magneticfield strength of the tangential field component Bt (FIG. 15) and theradial field component Br (FIG. 14) for this magnet differ only about10%, thus the two solutions offer substantially the same performance(accuracy, resolution) for a same distance r2 between the sensorelements and the rotation axis 4.

An arrangement with a six-pole ring magnet will be explained next, inrelation to FIG. 16 to FIG. 22.

FIG. 16 shows a six-pole ring-magnet 5 with a central cylindricalopening, as an example. A six-pole disk magnet with circular or polygonshape could alternatively also be used. The magnet 5 generates aperiodically repetitive magnetic field pattern B around the rotationaxis 4 in the vicinity of the magnet. Some magnetic field lines areshown on the outside of the ring-magnet, although the magnetic field Bis not measured on the outside of the ring, but rather “below” and “onthe inside” of the central magnet opening, in a plane β perpendicular tothe rotation axis 4 and at an axial distance d1 from the magnet surface,similar as in the arrangement shown in FIG. 6, but now for a six-polemagnet. Three bold black arrows indicate the orientation (not theposition) of a first group S of three sensor elements (not shown). Thesignals generated by them are indicated by S1, S2, S3. Tree bold whitearrows indicate the orientation of a second group T of three sensorelements (not shown), for generating signals T1, T2, T3.

The measurement of the radial and tangential field components could bebased on the principle of 3-phase sine-cosine sensing. The followingequations are valid for such a measurement:

S1=Bmag*sin(3α)+Bext*Cos(φext−2π/3);  (13)

S2=Bmag*sin(3α)+Bext*Cos(φext−4π/3;)  (14)

S3=Bmag*sin(3α)+Bext*Cos(φext;)  (15)

T1=Bmag*cos(3α)+Bext*Cos(φext−5π/6);  (16)

T2=Bmag*cos(3α)+Bext*Cos(φext−3π/2);  (17)

T3=Bmag*cos(3α)+Bext*Cos(φext−π/6);  (18)

where Bmag represents the magnitude of the magnetic field to be measured(e.g. the field created by the six-pole magnet 5), and Bext representsthe magnitude of a unidirectional external magnetic field under an angleφext with respect to the stator.

And:

sum1=S1+S2+S3=3*Bmag*sin(3α);  (19)

sum2=T1+T2+T3=3*Bmag*cos(3α);  (20)

and:

ratio R=sum1/sum2=tg(3α),  (21)

thus the magnitude of the constant magnetic field Bext is eliminated.

FIG. 17 shows the six sensor elements VH1 to VH6 adapted for measuringthe tangential field component Bt of the magnetic field at the imaginarycircle 8 located in the plane β. The sensor 6 can be implemented byusing so called “vertical Hall plate” sensor elements which aresensitive in the direction of the indicated arrows. In an example wherethe six-pole magnet 5 has an outer diameter of 12 mm, the imaginarycircle may have a diameter d2 between 0 and about 3 mm. No simulationsare reproduced here for this six-pole magnet, but results very similarto those of FIG. 7 and FIG. 9 and FIG. 11 are achieved, except that thefield shows six “black” areas instead of four. And a plot of the fieldstrength of the tangential or radial or axial field component Bt, Br,Bz, yields plots very similar to those of FIG. 13, FIG. 14 and FIG. 15,from which the position and/or maximum size of the “linear region” couldbe determined.

Referring back to FIG. 17, the angular position α is to be calculatedfrom these sensor elements as follows. The sensor elements VH1 to VH6are organized in two groups S, T of three elements each (in general, fora magnet with Np poles, each group of sensor elements would consist ofNp/2 sensor elements). The first group S has the sensor elementsproviding the signals S1, S2 and S3. The sensor elements VH1, VH2, VH3of this group S are located on the imaginary circle, at 120° angulardistance from one another. In general, for a magnet with Np poles, thisangular distance would be 720°/Np. The second group T has the sensorelements providing the signals T1, T2 and T3. The sensor elements VH4,VH5, VH6 of this group T are also located on the imaginary circle, at120° angular distance from each other. The distance between a sensorelement VH1 of the first group S and a sensor element VH4 of the secondgroup T, is 180°/Np=30°, with Np=6 for a six-pole magnet. The sameangular distance can be seen between VH2 and VH5, and between VH3 andVH6. In general, for a magnet with Np poles, the angular distancebetween elements of the different groups S, T would be 180°/Np. Then afirst sum sum1 is calculated as the sum of the signals S1, S2, S3generated by the sensor elements of the first group S:

sum1=S1+S2+S3˜sin(3α),  (22)

whereby “˜” means “is proportional to”.And a second sum sum2 is calculated as the sum of the signals T1, T2, T3generated by the elements of the second group T:

sum2=T1+T2+T3˜cos(3α)  (23)

One can then calculate a ratio R as:

R=sum1/sum2=tan(3α)  (24)

and the angle α can then be calculated as:

α=(arctan R)/3  (25)

In embodiments of the present invention, the sensor 6 may be anintegrated circuit, e.g. implemented in CMOS technology, and the meansfor calculating the angle α may be embedded on the same chip. Such achip may further include analog-to-digital convertors (not shown) fordigitizing the measured signals Si, Ti, and a digital signal processor(DSP) provided with an algorithm for calculating the angle α based onthe formulas described above, or equivalent formulas, or tables, or inany other way known by the person skilled in the art.

It is to be noted that instead of calculating the sum of the values of agroup, one could also calculate the average value of each group, and theratio of the averages, etc, which would yield the same result for theratio R and for the angle α.

The configuration of FIG. 17 is insensitive to offset errors of thesensor 6, because the signals generated by VH1, VH2, VH3 compensate eachother. The same applies for the sensor elements VH4, VH5, VH6. Theconfiguration of FIG. 17 is also insensitive to a uniform externalmagnetic field Bext, because the values measured by the sensor elementsin each group S, T cancel each other, due to the 120° rotation of thesensor elements. Due to the fact that a ratio is taken of the sum oraverage of the field components, the absolute value of the magneticfield components is irrelevant, only their relative values matter. Thismeans that the method is highly robust against ageing, tolerances onmagnets, and temperature. The angular position range which can bemeasured by the sensor elements VH1 to VH6 shown in FIG. 17 using the6-pole magnet of FIG. 16 is 120°. In general, for a magnet with Nppoles, the angular range is 720°/Np.

It is to be noted that the sensor elements of each group, e.g. theelements VH1, VH2, VH3 of the first group S, form a regular polygon(instead of being located in pairs on opposite diametrical sides of thecircle). In FIG. 17 the polygon is a triangle. This geometrical conceptcan be extended to sensors for measuring multi-pole magnets with morethan six poles, e.g. for a magnet with eight poles (Np=8), the sensorelements would be located on a square. The triangle for the sensorelements VH4, VH5, VH6 of the second group T is not shown for not makingthe drawing obscure. But it is easy to see that, in the embodimentillustrated, the position of the T-triangle (triangle formed by thegroup of elements VH4, VH5, VH6) can be easily obtained by rotating theS-triangle (triangle formed by the group of elements VH1, VH2, VH3) over180°/Np=30° in this example, since Np=6 for a six-pole magnet.

FIG. 18 shows an example of the combined sine and cosine signals, e.g.of the sum signals sum1 and sum2 (or of the average signals avg1 andavg2), which can be obtained from the groups S, T of the sensor elementsof FIG. 17, when being rotated with respect to the ring magnet. Asindicated, the phase difference between the two sum-signals is 30°, andthe signals have a period of 120°, which is the maximum angular range ofa which can be measured by the sensor of FIG. 17.

FIG. 19 shows another embodiment of a sensor 6 for measuring thetangential field components Bt of the six-pole ring-magnet shown in FIG.16. This sensor 6 looks like the sensor 6 shown in FIG. 17, except thateach vertical Hall plate sensor element VHi is replaced by a pair of twoadjacent horizontal Hall plate elements and Integrated MagneticConcentrators (in short IMC). The IMC converts a magnetic field parallelwith the chip surface locally into a field perpendicular to the surface,or in other words, converts the tangential and radial field componentsBt, Br into an axial field component Bz. The perpendicular component ofthe magnetic field is then sensed by conventional planar Hall elements(also called “horizontal Hall plate” elements). A magnetic concentratoralso functions as a passive magnetic amplifier and improves sensorperformance.

The signals H1, H2, of the pair of adjacent sensor elements aresubtracted, so as to form a single signal S1. During the same operationany Bz field from an external (unwanted) field is subtracted, so that itdoes not impact the reading of S1. The same applies for the signalsobtainable from the other pairs.

It is to be noted that the IMC makes an additional gain, but it alsorotates the local tangential field component (flux-lines) into an axialdirection, substantially perpendicular to the horizontal Hall elementsGi, Hi (i=1 to 6). The former is indicated hereinafter by amultiplication (*IMC), but the latter cannot be expressed by a formulain a simple manner. Thus S1=(H1−H2)˜the strength of the tangential fieldBt (at the location of VH1 of FIG. 17) multiplied by the factor IMC, orS1=(H1−H2)*IMC. It is to be noted that the abbreviation IMC is usedherein to indicate the integrated magnetic concentrator itself, or itsamplification value. It will be clear from the context which one of bothmeanings is intended. Likewise S2=(H3−H4)*IMC, S3=(H5−H6)*IMC,T1=(G1−G2)*IMC, T2=(G3−G4)*IMC and T3=(G5−G6)*IMC. From these signals Siand Ti, the first and second sum1, sum2 (or first and second average)can be calculated as described before, and the ratio R, and the angle α.It is an advantage of this embodiment that “horizontal hall plate”elements can be used, which are about 2-4 times more sensitive(depending on the technology applied) and which feature an offset (andoffset drift with temperature and lifetime) which is about 5-10 timessmaller than “vertical” Hall elements.

It is to be noted that the arrangement of FIG. 19 does not measure theaxial component Bz of the magnetic field (as was illustrated in FIG. 11for a four-pole magnet).

Since the difference between two Hall plates which are close to one gapis built, the common mode part (Bz component) is eliminated. As for thedifferential part (e.g. the part of Bz which is different on H1 comparedto H2) it merely adds a harmonic signal with the same periodicity asradial/tangential field and is therefore just adding signal.

The IMC has some kind of periodicity, similar to the magnet field. Thedimensions of the IMC are: (a) thickness, which is determined by thetechnology, and (b) ring width, which is a question of design. Thicknessand width must be made such that on one hand they give a good, e.g. thehighest, gain on the Hall devices, but on the other hand there must notbe saturation effects from the magnetic field bringing non-linearity.Suitable dimensions can be determined by routine tests, or by trial anderror.

FIG. 20 shows the same six-pole ring magnet with a central cylindricalopening as shown in FIG. 16. As before, the three bold black arrowsindicate the orientation of a first group S of three sensor elements(not shown in FIG. 20), and the three bold white arrows indicate theorientation of a second group T of three sensor elements (not shown inFIG. 20), all sensor elements being adapted for measuring the radialfield component Br. The signals generated by the sensor elements of thefirst group S are indicated by S1, S2, S3. The signals generated by thesensor elements of the second group T are indicated by T1, T2, T3.

FIG. 21 shows an embodiment of the position and orientation of sixvertical Hall sensor elements of a sensor 6 for determining an absoluteposition α using the six-pole ring magnet of FIG. 20. The sensorelements are located on an imaginary circle with diameter d2, andadapted for measuring the radial magnetic field component Br of themagnet of FIG. 20 in plane β at an axial distance d1 from the magnet,and in line with the rotation axis 4 of the magnet, as shown in FIG. 2.This is a variant of the embodiment shown in FIG. 17, and everythingwhich was said for the sensor 6 of FIG. 17 is also applicable for thesensor of FIG. 21, except for the orientation of the magnetic fieldcomponent, and the corresponding orientation of the sensor elements.

FIG. 22 shows an example of the combined sine and cosine signals sum1,sum2 which can be obtained from the sensor 6 of FIG. 21. It is to benoted that these signals are in principle identical to those of FIG. 18,but these signals are generated by measuring the radial field componentBr instead of the tangential field component Bt. Both solutions of FIG.17 and FIG. 21 are substantially equivalent with respect to accuracy,resolution, insensitivity to sensor position offset, and insensitivityto a constant external magnetic field Bext. This concept can be extendedto other multi-pole ring or disc magnets, having at least four magneticpoles, and a central cylindrical hole.

FIG. 23 shows an example of a sensor 6 having twelve vertical Hallsensor elements VH1 to VH12, oriented for measuring the radial magneticfield component Br of a six-pole magnet, e.g. the six-pole ring-magnetof FIG. 16. When comparing this sensor 6 with the sensor of FIG. 17 andFIG. 21, it is to be noted that the sensor of FIG. 23 has twice thenumber of sensor elements. In the example shown in FIG. 23, all sensorelements are oriented for measuring a radial field component Br, butthat is not absolutely required, and all or half of the elements couldbe oriented for measuring the tangential field components Bt. In thelast example, the sensor 6 would be seen as a combination of the sensorelements of the sensor shown in FIG. 17 and the one shown in FIG. 21.The redundancy may be used for improved accuracy, or an improvedposition-offset insensitivity, or improved rejection to irregularitiesof the magnet, or simply as a reliability check.

In accordance with embodiments of the present invention, the sensorelements are organized in four groups S, T, U, V of three sensorelements each, the number of sensor elements in a group being equal tohalf the number of poles Np of the magnet. The elements in each groupare distributed equidistantly, hence at an angular distance of 720°divided by the number of poles, thus 720°/Np=120°, since Np=6 for thesix-pole magnet. The elements of the first group S are thus VH12, VH4and VH8, the elements of the second group T are VH3, VH7, VH11. Theelements of the third group U are VH2, VH6, VH10. The elements of thefourth group V are VH1, VH5, VH9.

The elements of the second group T are located at the positions whichwould be taken when the elements of the first group S are rotated over180°/Np, e.g. 30° for a six-pole magnet in the example of FIG. 23. Theelements of the third group U are located at the positions which wouldbe taken when the elements of the first group S are rotated over2×(180°/Np), e.g. 2×30°=60°. The elements of the fourth group V arelocated at the positions which would be taken when the elements of thefirst group S are rotated over 3×(180°/Np), e.g. 3×30°=90°.

The first group S could comprise the sensors VH12, VH4 and VH8, andtheir signals S1, S2, S3 would be added to form a combined signal sum1.The second group T could comprise the sensors VH3, VH7 and VH11, andtheir signals T1, T2, T3 would be added to form a combined signal sum2.The third group U could comprise the sensors VH2, VH6 and VH10, andtheir signals U1, U2, U3 would be added to form a combined signal sum3.The fourth group V could comprise the sensors VH1, VH5 and VH9, andtheir signals V1, V2, V3 would be added to form a combined signal sum4.

A first angle α1 could then e.g. be calculated as[arctan(sum1/sum2)]/3+offset1, and a second angle α2 could then e.g. becalculated as [arctan(sum3/sum4)]/3+offset2, whereby offset1 and offset2 can be determined during manufacturing, e.g. by calibration. Thevalues offset2 and offset1 would typically vary by about 60°. Dependingon the application, these angles α1 and α2 could be averaged to form asingle angle α, or the two angles α1 and α2 could be compared, and iftheir values differ above a given threshold, an error signal could beprovided by the sensor, as an indication of a problem.

It is to be noted that in the drawings the second, third and fourthgroup T,U,V are rotated in counter-clockwise direction with respect tothe first group S, but they could also be rotated in clock-wisedirection. The formulas for calculating the angle would be identical,but the resulting angular position of the rotor w.r.t. the stator wouldbe measured in the opposite direction. However, such a sensor and methodwould yield the same advantages.

Second Algorithm

Another aspect of the present invention will be explained with referenceto FIG. 23 to FIG. 28. It is to be noted that FIG. 23 is used todescribe two different embodiments, depending on which formulas are usedto calculate the angular position. Most embodiments described above, arerobust for a uniform external magnetic field Bext, e.g. a field having aconstant amplitude and a constant direction, as indicated by the arrowsin FIG. 2. Most of the embodiments described above, are also robustagainst position offset errors, however, none of these embodiments isrobust against a non-uniform external magnetic field.

After years of ongoing research in the domain of angle sensors, theinventors have surprisingly found that it is also possible to eliminate,or at least partially compensate for a magnetic field having a constantgradient. This means that the external magnetic field and/or a magneticfield component may vary in a linear way in the X and/or Y and/orZ-direction without substantially influencing the measured angle.

FIG. 24 shows a typical example in an automotive application, where theangular position sensor 6 is located in the vicinity of a currentcarrying conductor. It is well known that the magnitude of a magneticfield around such a current carrying conductor can be described by theformula:

H=I/2πr  (26)

where I is the current running through the conductor, r is the distancefrom the conductor at which the field is observed, and B or H are bothused to describe the magnetic field, whereby B=μ·H, where μ is amaterial (or medium) dependent value. Over a small area located at apredefined non-zero distance from the wire, e.g. over the small areadefined by the sensor 6, the magnetic field caused by the current in thewire can be approximated by a constant field plus a constant fieldgradient.

In contrast to FIG. 2 where the external field Bext is constant on alllocations of the sensor chip, the magnetic field Bext of FIG. 24 is notconstant over the sensor chip. Only when the sensor chip is at arelatively large distance with respect to the conductor, the externalfield can be approximated by its zero-order term, that is a constantvector (Bxo, Byo, Bzo).

However, when the sensor chip is closer to the conductor, the zero-orderterm is not a good approximation anymore. It can be seen, that themagnitude of such a field is proportional to 1/r. So the field containsa gradient which is nonlinear. As an example, when the angular positionsensor is placed at a distance of 25.0 mm from a straight currentconductor carrying I=400 A, the sensor will see a magnetic flux densityof about 3.2 mT generated by this current. If the sensor has a physicaldimension of about 1.0 mm, then the part of the sensor closer to theconductor sees a field of 3.14 mT and the part further from theconductor sees a field of 3.27 mT. The external field can thus not beconsidered constant over the sensor surface, but over such a smalldistance of 1.0 mm at a relatively large distance of 25.0 mm, the fieldcan be approximated by its zero order and first order terms, while thesecond and higher order terms are negligible. In other words, a constantvalue plus a constant (three-dimensional) gradient. The inventors havenow surprisingly found that it is possible to substantially compensatenot only for the zero-order term (the uniform field as discussed above),but also for these first order terms (the constant gradient), as will bedescribed next.

A first arrangement which is capable to substantially compensate forsuch a constant gradient is the configuration of FIG. 23, in combinationwith a six-pole permanent magnet (e.g. the 6-pole ring-magnet shown inFIG. 20), but by using the following equations to calculate the angularposition:

sin(3α)=(S1+S2+S3)−(U1+U2+U3);  (27)

cos(3α)=(T1+T2+T3)−(V1+V2+V3);  (28)

ratio=sin(3α)/cos(3α)=tan(3α);  (29)

α=(arctan ratio)/3;  (30)

Alternatively, the following equivalent set of formulas can be used:

sum1=S1+S2+S3;  (31)

sum2=T1+T2+T3;  (32)

sum3=U1+U2+U3;  (33)

sum4=V1+V2+V3;  (34)

diff1=sum1−sum3;  (35)

diff2=sum2−sum4;  (36)

ratio=diff1/diff2=tan(3α);  (37)

α=(arctan ratio)/3;  (38)

This position sensor 6 has twelve vertical Hall sensing elements VH1 toVH12, adapted for measuring the radial field component (Br) of asix-pole magnet, as shown in FIG. 20. In the embodiment illustrated, thesensor elements are partitioned in four groups S, T, U, V of threeelements each. In general the number of elements in a group equals thenumber of magnet poles Np divided by two. The elements within eachgroup, e.g. VH12, VH4, VH8 in the first group S, are located at anangular distance of 120° apart (in general: 720°/Np). The elements ofthe second group T are located at the positions which the elements ofthe first group S would assume after rotation over 180°/Np, e.g. 30°when Np=6 (six-pole magnet). The elements of the third group U arelocated at the positions which the elements of the first group S wouldassume after rotation over 360°/Np, e.g. 60° when Np=6. The elements ofthe fourth group V are located at the positions which the elements ofthe first group S would assume after rotation over 540°/Np, e.g. 90°when Np=6. The position sensor has means for calculating the angularposition α according to the above formulas (27) to (38), or equivalentformulas.

Simulations have shown that such a sensor has the followingcharacteristics:

1) the position α thus determined is substantially insensitive (or atleast has a reduced sensitivity) to position offset.

2) the position α thus determined is substantially insensitive (or atleast has a reduced sensitivity) to a constant external magnetic field.

3) the position α thus determined is substantially insensitive (or atleast has a reduced sensitivity) to an external magnetic field having asubstantially constant gradient, e.g. that changes linearly in any ofthe X, Y, Z directions. As far as known to the inventors, this technicaleffect is not obtained by prior art angular position sensors. Such asensor is ideal for industrial or automotive applications, where anangular position needs to be accurately determined, even in environmentswhere unwanted magnetic fields are present, such as caused by currentsflowing in (relatively) nearby conductors.

FIG. 25 shows another embodiment of an angular position sensor withtwelve sensor elements VH1 to VH12, arranged at equidistant positions ona virtual circle, to be used in conjunction with a six pole ring magnetor six pole disk magnet. This position sensor 6 has twelve vertical Hallsensing elements VH1 to VH12, adapted for measuring the tangential fieldcomponent Bt of a six-pole magnet, as shown in FIG. 16. In theembodiment illustrated, the sensor elements VH1 to VH12 are partitionedin four groups S, T, U, V of three elements each. In general, when theelements are partitioned in four groups, the number of elements in agroup equals the number of poles divided by two. The elements withineach group, e.g. VH12, VH4, VH8 in the group S, are located at anangular distance of 120° apart (in general: 720°/Np). The elements ofthe second group T are located at the positions which the elements ofthe first group S would assume after rotation over 180°/Np, e.g. 30° asNp=6 for a six-pole magnet. The elements of the third group U arelocated at the positions which the elements of the first group S wouldassume after rotation over 360°/Np, e.g. 60°. The elements of the fourthgroup V are located at the positions which the elements of the firstgroup S would assume after rotation over 540°/Np, e.g. 90°.

The same formulas as were used for the embodiment of FIG. 24 can be usedto calculate the angular position α:

sin(3α)=(S1+S2+S3)−(U1+U2+U3);  (39)

cos(3α)=(T1+T2+T3)−(V1+V2+V3);  (40)

ratio=sin(3α)/cos(3α)=tan(3α);  (41)

α=(arctan ratio)/3;  (42)

And the sensor has the same advantages of i) being substantiallyinsensitive to position offset, and ii) to a constant external magneticfield, and iii) to a constant external field gradient.

FIG. 26 shows another embodiment of an arrangement with twelve magneticsensing elements, as can be used in a magnetic angular position sensor,which is substantially insensitive to position offset, and to a constantexternal magnetic field, and to a constant external field gradient. Inthis embodiment, the magnetic sensing elements are so-called horizontalHall elements arranged at equidistant positions on a circle, but inaddition the sensor further comprises an integrated magneticconcentrator (abbreviated as IMC). The IMC comprises a central part 11located on top of the horizontal Hall elements, and a plurality ofelongated parts 10, e.g. trapezoidal shaped strips, located at adistance from the Hall element and oriented in radial directions. Theprinciple of using magnetic concentrators for bending the radial andtangential magnetic field lines is known a.o. from US20020021124.Suitable, e.g. optimal, shape and dimensions (e.g. length, width,thickness) of these concentrators can be experimentally determined. Inthe example shown, the concentrator comprises a center disk and twelvetrapezoidal “sun-rays” around the center disk, one “sun-ray” per Hallsensor. Such integrated magnetic concentrators IMC can be applied as apost-process when fabricating the sensor device. Due to the localdeflection of the magnetic field by the IMC, the Hall elements HH1, etc.measure the combination of the radial component Br and the verticalcomponent Bz (vertical to the plane of the Figure). The radial componentBr is amplified due to the IMC by a factor which is typically in therange between 1 and 10, depending on the exact IMC geometry, while theBz component is subtracted from it. So the Hall voltage Vh generated byeach Hall element is for example Vh=SE×(5 Br−Bz) with SE being the Hallelement sensitivity.

FIG. 27 shows a variant of the embodiment of FIG. 26, whereby the Hallelements are positioned under the inner edge of the elongatedconcentrators (“sun-rays”). In this case the Hall elements again measurethe radial field component Br with a certain gain between 1 and 10, andalso measure the vertical component Bz. But, compared to the embodimentof FIG. 26, the Bz component now has the opposite sign. So, the Hallvoltage generated by each element would be Vh=SE×(5 Bx+Bz) with SE beingthe Hall element sensitivity.

In mathematical terms, the insensitivity to a constant external magneticfield, and to a constant magnetic field gradient, may be described asfollows. Reference is made to FIG. 24. In practice there may be manyexternal sources causing an external field, but for the sake of thediscussion below, only the magnetic field Bext caused by the currentflowing in the conductor is considered. The magnetic field Bext is athree-dimensional function, depending on the location (x,y,z). Locally,over the sensor area of the angular position sensor, this field can beapproximated by its zero and first order terms, as expressed by thefollowing formula:

$\begin{matrix}{B_{s} = {\begin{pmatrix}{Bx}_{0} \\{By}_{0} \\{Bz}_{o}\end{pmatrix} + {\begin{pmatrix}\frac{{Bx}}{x} & \frac{{Bx}}{y} & \frac{{Bx}}{z} \\\frac{{By}}{x} & \frac{{By}}{y} & \frac{{By}}{z} \\\frac{{Bz}}{x} & \frac{{Bz}}{y} & \frac{{Bz}}{z}\end{pmatrix} \cdot \begin{pmatrix}x_{s} \\y_{s} \\z_{s}\end{pmatrix}}}} & (43)\end{matrix}$

where (Bxo, Byo, Bzo) is a three-dimensional (constant) vector formed bythe zero-order term of the function, and dBn/dm are the field gradientsfor n=x, y, z and m=x, y, z, and (xs, ys, zs) are the coordinates on thesensor chip.

If the sensor plane is defined as z=0 (e.g. if we position the X, Y, Zaxes as shown in FIG. 24), the equation reduces to:

$\begin{matrix}{B_{s} = {\begin{pmatrix}{Bx}_{0} \\{By}_{0} \\{Bz}_{o}\end{pmatrix} + {\begin{pmatrix}\frac{{Bx}}{x} & \frac{{Bx}}{y} & \frac{{Bx}}{z} \\\frac{{By}}{x} & \frac{{By}}{y} & \frac{{By}}{z} \\\frac{{Bz}}{x} & \frac{{Bz}}{y} & \frac{{Bz}}{z}\end{pmatrix} \cdot \begin{pmatrix}x_{s} \\y_{s} \\0\end{pmatrix}}}} & (44)\end{matrix}$

where dBx/dx, dBx/dy, dBx/dz, dBy/dx, etc are constants.

All embodiments explained above with reference to FIG. 23 to FIG. 27 andwherein the angle is calculated according to formula (27) or higher,have in common that by the combination of the signals of the twelvesensor elements as indicated,

1) Any homogeneous external magnetic field with vector (Bx0, By0, Bz0)is substantially cancelled out (or at least reduced) and does notdisturb the measurement of the angular position, but in addition,2) Any constant gradient field is also substantially cancelled out (orat least reduced) and does not disturb the angle measurement.

Simulation results using an arrangement as shown in FIG. 24, and aconfiguration of twelve Hall sensors as shown in FIG. 25 and theformulas (39) to (42) have surprisingly shown that the DC-component issubstantially completely eliminated, while the first order coefficientsdBn/dm were reduced by at least a factor of two, preferably at least afactor five, more preferably at least a factor ten. In a particularsimulation, with a current of 400 A running through a conductor, themagnetic field at a distance of 25 mm is 3.2 mT, and the magnetic fieldgradient is 130 μT/mm (microTesla per mm). Thus a classical sensor witha size of 1 mm would measure a remaining error signal of 130 μT.Accurate finite element simulations have demonstrated that by using thesensor of FIG. 25 in combination with the formulas [39] to [42], theremaining error signal was reduced to below 5 μT, which was thesimulation noise level. This may be explained as follows: The cancelingout of the zero-order term seems to be due to the fact that the value oftwo groups having the same “center of gravity” and the same amplitude(same radius) are subtracted, yielding a zero result. The canceling outof the gradient (first order term) seems to be comparable to three-phasealternating current. Any potential gradient direction corresponds to aspecific moment in the three phase period, but no matter which moment islooked at, the sum of the three phases is always zero.

It is clear that the main advantage of such a sensor is that it canmeasure the position with an improved accuracy, even in the presence ofan external magnetic field caused by a current flowing in one or moreconductors, such as is the case “under the hood” of a vehicle.

FIG. 28 shows another embodiment of the present invention, where theposition sensor 6 has eight horizontal Hall elements HH1 to HH8, but nomagnetic concentrator is used, hence these Hall elements are sensitiveto the vertical field Bz component. This sensor is to be used togetherwith a four-pole ring magnet, an example of which is shown in FIG. 6.FIG. 11 shows an example of the vertical field components Bz provided bysuch a magnet.

The eight Hall elements HH1 to HH8 are divided in four groups S, T, U,V, each group comprising half the number of poles of the magnet, hence 2elements (Np=4 for the four-pole magnet). The elements in each group aredistributed equidistantly, hence at an angular distance of 720°/Np=180°.The elements of the second group T are located at the positions whichwould be taken when the elements of the first group S are rotated over180°/Np or 45° in this example. The elements of the third group U arelocated at the positions which would be taken when the elements of thefirst group S are rotated over 2×180°/Np, or 90° in this example. Theelements of the fourth group V are located at the positions which wouldbe taken when the elements of the first group S are rotated over3×180°/Np, or 135° in this example.

The angular position between the sensor and the rotor is calculated asfollows:

sum1=S1+S2  (45)

sum2=T1+T2  (46)

sum3=U1+U2  (47)

sum4=V1+V2  (48)

diff1=sum1−sum3  (49)

diff2=sum2−sum4  (50)

ratio=diff1/diff2=tan(2α);  (51)

and the angle α can then be calculated as:

α=(arctan R)/2  (52).

Simulations have shown that this sensor has the followingcharacteristics:

1) the position α thus determined is substantially insensitive (or atleast has a reduced sensitivity) to position offset, (even though notperfect if the diameter of the imaginary circle is too small, asdiscussed in relation with FIG. 13),2) the position α thus determined is substantially insensitive (or atleast has a reduced sensitivity) to a constant external magnetic field,3) the position α thus determined is substantially insensitive (or atleast has a reduced sensitivity) to “some” constant field gradients, inparticular dBz/dx and dBz/dy, but in contrast to the six-pole magnet,not to the other first order terms: dBx/dx, dBx/dy, dBy/dx and dBy/dy.Nevertheless, this embodiment is still an improvement of prior artsensors, which do not compensate against any field gradient.

Preliminary simulations seem to indicate that the advantages obtained bythe sensor of FIG. 25 (with twelve sensor elements in combination with asix-pole magnet) can also be obtained with an eight-pole magnet incombination with sixteen Hall-elements, or a ten-pole magnet and twentyHall-elements, partitioned in four groups arranged in a similar manneras above, and using formulas similar to [39] to [42] as described above,but slightly adapted to take into account the different number ofelements per group. Indeed, an eight-pole magnet would be measured bysixteen sensor elements, partitioned in four groups S, T, U, V, eachgroup having 4 sensor elements located at an equidistant angle of360°/4=90° on a virtual circle, the elements of the second group T beinglocated at the positions which would be assumed when the elements of thefirst group S would be rotated over 180°/Np=22.5° since Np=8 for aneight-pole magnet. The elements of the third group U being located atthe positions which would be assumed when the elements of the secondgroup T would be rotated over another 180°/Np=22.5°, and the elements ofthe fourth group V being located at the positions which would be assumedwhen the elements of the third group U would be rotated over another180°/Np=22.5°. A disadvantage of a configuration with eight poles,however, is that the angular range is reduced to the range from 0° to90°, and that the dimensions and tolerances of the magnet decrease asthe number of poles increases.

But the invention is not limited to an eight-pole, and in a similarmanner, the magnetic field caused by a ten-pole magnet could be measuredby twenty sensor elements, partitioned in four groups S, T, U, V, eachgroup having 5 sensor elements located at an equidistant angle of360°/5=72° on a virtual circle, the elements of the second group T beinglocated at the positions which would be assumed when the elements of thefirst group S would be rotated over 180°/Np=18° since Np=10 for aneight-pole magnet. The elements of the third group U being located atthe positions which would be assumed when the elements of the secondgroup T would be rotated over another 18°, and the elements of thefourth group V being located at the positions which would be assumedwhen the elements of the third group U would be rotated over another18°.

The following table summarizes the most important features of severalenvisioned sensors with a 4-pole and 6-pole ring magnet, most of whichembodiments are described in detail above. Some simulations and testsare still ongoing.

TABLE 1 sensitivity nr of sensor orientation sensitivity sensitivityconstant nr of magnet elements + of the sensor position constant extfield poles Np (groups) algorithm elements error ext field gradient 4(*1) 4(S, T) algorithm1 Br s-ins s-ins yes 4 (*1) 4(S, T) algorithm1 Bts-ins s-ins yes 4 (*1) 4(S, T) algorithm1 Bz some yes yes 4 (*2) 8(S, T,U, V) algorithm2 Br s-ins s-ins yes 4 (*2) 8(S, T, U, V) algorithm2 Bts-ins s-ins yes 4 (*3) 8(S, T, U, V) algorithm2 Bz some s-ins s-not 66(S, T) algorithm1 Br s-ins s-ins yes 6 6(S, T) algorithm1 Bt s-inss-ins yes 6 6(S, T) algorithm1 Bz some s-ins yes 6 12(S, T, U, V)algorithm1 Br s-ins s-ins yes 6 12(S, T, U, V) algorithm1 Bt s-ins s-insyes 6 12(S, T, U, V) algorithm2 Br s-ins (*4) s-ins s-ins 6 12(S, T, U,V) algorithm2 Bt s-ins (*4) s-ins s-ins 6 12(S, T, U, V) algorithm2 Bzsome (*4) s-ins s-ins wherein “s-ins” stands for “substantiallyinsenstive”, and wherein algorithm1 is based on the formula:arctan(Σ(Si)/Σ(Ti)) described above, as exemplified for example by theformulas [22] to [25], and wherein algorithm2 is based on the formula:arctan((Σ(Si) − Σ(Ui))/(Σ(Ti) − Σ(Vi)) as described above, asexemplified for example by the formulas [39] to [42]. (*1) Thisstructure is not robust to gradients. (*2) This structure is not robustto Bx and By gradients. (*3) This structure is robust to all gradients,since here Bx and By have no impact. Only Bz is measured and constantgradients on Bz are cancelled. (*4) Preliminary tests point out that theoff-axis situation is not completely robust. It is however quite good upto 0.7 mm, but then angle errors are increasing.

1-31. (canceled)
 32. An arrangement for measuring an angular position ofa rotor with respect to a stator, the arrangement comprising: the rotorrotatable around a rotation axis; the stator having a fixed positionwith respect to the rotation axis; a magnetic source mounted on therotor for creating a magnetic field, the magnetic source being amulti-pole magnet having a number of magnetic poles for generating aperiodically repetitive magnetic field pattern with respect to therotation axis, the number of magnetic poles being at least four; asensor mounted on the stator and comprising a plurality of sensorelements for measuring at least one magnetic field component of themagnetic field and for providing a measurement signal indicative of theat least one magnetic field component, the number of sensor elementsbeing twice the number of magnetic poles of the multi-pole magnet, thesensor being located centered around the rotation axis and being locatedin a plane perpendicular to the rotation axis at a first distance fromthe magnetic source; the sensor elements being located on a circle at asecond distance from the rotation axis, and being oriented for detectingthe at least one magnetic field component; the plurality of sensorelements being partitioned in at least a first group and a second groupand a third group and a fourth group, the elements within each groupbeing located at equidistant angular positions on the circle, theangular distance between an element of the first group and an element ofthe second group being equal to 180° divided by the number of magneticpoles of the magnetic source, the angular distance between an element ofthe third group and an element of the first group being equal to 360°divided by the number of magnet poles of the magnetic source, and theangular distance between an element of the fourth group and an elementof the first group being equal to 540° divided by the number of magnetpoles of the magnetic source; means for calculating the angular positionof the rotor from the provided signals, the means for calculating beingadapted for calculating a first sum or first average of the signalsprovided by the sensor elements of the first group, and for calculatinga second sum or second average of the signals provided by the sensorelements of the second group, and for calculating a third sum or thirdaverage of the signals provided by the elements of the third group, andfor calculating a fourth sum or fourth average of the signals providedby the elements of the fourth group, and for determining the angularposition of the rotor based on one or more values selected from thegroup consisting of the first sum, first average, the second sum and thesecond average, the third sum, the third average, the fourth sum and thefourth average.
 33. The arrangement according to claim 32, wherein themulti-pole magnet is a permanent magnet.
 34. The arrangement accordingto claim 33, wherein the multi-pole magnet has at least six magneticpoles.
 35. The arrangement according to claim 33, wherein the multi-polemagnet has a ring shape having an outer diameter and an inner diameter,and wherein the circle in the sensor has a diameter of 1 to 30% of theouter diameter of the magnet.
 36. The arrangement according claim 32,wherein the measured at least one magnetic field component comprises atangential field component of the magnetic field, oriented tangential tothe circle.
 37. The arrangement according to claim 36, wherein thesensor elements comprise vertical Hall effect elements having a platewith a normal that is tangential to the circle.
 38. The arrangementaccording to claim 36, wherein each sensing element comprises a pair ofhorizontal Hall effect elements adapted for providing signals and beinglocated on the circle adjacent to each other, and having plates orientedperpendicular to the rotation axis, and IMC segments for bending thelocal tangential magnetic field into a direction perpendicular to theplates.
 39. The arrangement according to claim 33, wherein the measuredat least one magnetic field component comprises a radial field componentof the magnetic field, oriented radially to the circle, and wherein thesensor elements comprise vertical Hall effect elements having a platewith a normal that is perpendicular to and intersects with the rotationaxis.
 40. The arrangement according to claim 32, wherein each sensorelement comprises a horizontal Hall effect element and wherein thearrangement further comprises an integrated magnetic concentratorcomprising a central part located on top of the horizontal Hall elementsand a plurality of elongated parts located at a distance from the Hallelements and oriented in radial directions; or wherein each sensorelement comprises a horizontal Hall effect element and wherein thearrangement further comprises an integrated magnetic concentratorcomprising a central part and a plurality of elongated parts eachlocated on top of one of the Hall elements and oriented in radialdirections.
 41. The arrangement according to claim 32, wherein the meansfor calculating is further adapted for calculating a first differencebetween the first sum and the third sum, and for calculating a seconddifference between the second sum and the fourth sum; and wherein themeans for calculating is further adapted for calculating the ratio ofthe first difference and the second difference, and for determining theangular position of the rotor based on the arctangent or arc cotangentof said ratio.
 42. Method for determining an angular position of a rotorwith respect to a stator using the arrangement according to claim 32,comprising: calculating a first sum or a first average of the signalsprovided by the first group of sensor elements; calculating a second sumor second average of the signals provided by the second group ofelements; calculating a third sum or third average of the signalsprovided by the sensor elements of the third group of elements;calculating a fourth sum or fourth average of the signals provided bythe sensor elements of the fourth group of elements; determining theangular position of the rotor based on one or more numbers selected fromthe group consisting of the first sum, the first average, the secondsum, the second average, the third sum, the third average, the fourthsum and the fourth average.
 43. The method according to claim 42,wherein the measured at least one magnetic field component comprises atangential field component of the magnetic field, oriented tangential tothe circle, and wherein each sensing element comprises a pair ofhorizontal Hall effect elements adapted for providing signals and beinglocated on the circle adjacent to each other, and having plates orientedperpendicular to the rotation axis, and IMC segments for bending thelocal tangential magnetic field into a direction perpendicular to theplates; the method further comprising the step of subtracting thesignals of the elements of each pair so as to provide a combined signalfor the calculation of the first resp. second, third, fourth sum orfirst resp. second, third, fourth average.
 44. The method according toclaim 42, further comprising the step of calculating a first differencebetween the first sum and the third sum, and calculating a seconddifference between the second sum and the fourth sum, and calculatingthe ratio of the first difference and the second difference, anddetermining the angular position of the rotor based on the arctangent orarc cotangent of said ratio.
 45. An integrated sensor circuit formeasuring an angular position of a rotor with respect to a stator, therotor being rotatable around a rotation axis and comprising a magneticsource mounted on the rotor for creating a magnetic field, the magneticsource being a multi-pole magnet having a number of magnetic poles forgenerating a periodically repetitive magnetic field pattern with respectto the rotation axis, the number of magnetic poles being at least four;the stator having a fixed position with respect to the rotation axis,the integrated sensor circuit being mountable to the stator in thevicinity of the multi-pole magnet and in line with the rotation axis ina plane perpendicular to the rotation axis at a first distance from themagnetic source, the integrated sensor circuit comprising: a pluralityof sensor elements, the number of sensor elements being twice the numberof magnetic poles of the multi-pole magnet, each sensor element beingadapted for measuring at least one magnetic field component of themagnetic field and for providing a measurement signal indicative of thestrength of the at least one magnetic field component at the location ofthe sensor element, the sensor elements being located on a circle at adistance from the rotation axis, and being oriented for detecting the atleast one magnetic field component; the plurality of sensor elementsbeing partitioned in a first group and a second group and a third groupand a fourth group, the elements within each group being located atequidistant angular positions on the circle, the angular distancebetween an element of the first group and an element of the second groupbeing equal to 180° divided by the number of magnet poles of themagnetic source, the angular distance between an element of the thirdgroup and an element of the first group being equal to 360° divided bythe number of magnet poles of the magnetic source, and the angulardistance between an element of the fourth group and an element of thefirst group being equal to 540° divided by the number of magnet poles ofthe magnetic source; means for calculating the angular position of therotor from the provided signals; wherein: the means for calculatingbeing adapted for calculating a first sum or first average of thesignals provided by the elements of the first group, and for calculatinga second sum or second average of the signals provided by the elementsof the second group, and for calculating a third sum or third average ofthe signals provided by the elements of the third group, and forcalculating a fourth sum or fourth average of the signals provided bythe elements of the fourth group, and for determining the angularposition of the rotor based on one or more number selected from thegroup consisting of the first sum, first average, the second sum and thesecond average, the third sum, the third average, the fourth sum and thefourth average.
 46. The integrated circuit according to claim 45,wherein each sensor element comprises a vertical Hall effect elementhaving a plate with a normal that is tangential to the circle, or anormal that is perpendicular to and intersects with the rotation axis.47. The integrated circuit according to claim 45, wherein each sensingelement comprise a pair of horizontal Hall effect elements adapted forproviding signals and being located on the circle adjacent to eachother, and having plates oriented perpendicular to the rotation axis,and IMC segments for bending the local tangential magnetic field into adirection perpendicular to the plates.
 48. The integrated circuitaccording to claim 45, wherein each sensor element comprises ahorizontal Hall effect element and wherein the integrated circuitfurther comprises an integrated magnetic concentrator comprising acentral part located on top of the horizontal Hall elements and aplurality of elongated parts located at a distance from the Hallelements and oriented in radial directions; or wherein each sensorelement comprises a horizontal Hall effect element and wherein theintegrated circuit further comprises an integrated magnetic concentratorcomprising a central part and a plurality of elongated parts eachlocated on top of one of the Hall elements and oriented in radialdirections.
 49. The integrated circuit according to claim 45, whereinthe means for calculating is further adapted for calculating a firstdifference between the first sum and the third sum, and for calculatinga second difference between the second sum and the fourth sum; andwherein the means for calculating is further adapted for calculating theratio of the first difference and the second difference, and fordetermining the angular position of the rotor based on the arctangent orarc cotangent of said ratio.